Interferometry of Solar System Objects

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1 Interferometry of Solar System Objects Bryan Butler National Radio Astronomy Observatory Atacama Large Millimeter/submillimeter Array Expanded Very Large Array Robert C. Byrd Green Bank Telescope Very Long Baseline Array

2 Solar System Bodies Sun IPM Giant planets Terrestrial planets Moons Small bodies

3 Why Interferometry? resolution, resolution, resolution! maximum angular extent of some bodies: Sun & Moon o Venus 60 Jupiter 50 Mars 25 Saturn 20 Mercury 12 Uranus 4 Neptune Galilean Satellites Titan 1 Triton Pluto MBA NEA, KBO (interferometry also helps with confusion!)

4 Solar System Oddities Radio interferometric observations of solar system bodies are similar in many ways to other observations, including the data collection, calibration, reduction, etc So why am I here talking to you? In fact, there are some differences which are significant (and serve to illustrate some fundamentals of interferometry).

5 Differences Object motion Time variability Confusion Scheduling complexities Source strength Coherence Source distance Knowledge of source Optical depth

6 Object Motion All solar system bodies move against the (relatively fixed) background sources on the celestial sphere. This motion has two components: Horizontal Parallax - caused by rotation of the observatory around the Earth. Orbital Motions - caused by motion of the Earth and the observed body around the Sun.

7 Object Motion - an example

8 Object Motion - a practical example 1998 September September o 4C C Jupiter de Pater & Butler 2003

9 Time Variability Time variability is a significant problem in solar system observations: Sun - very fast fluctuations (< 1 sec) Jupiter, Venus (others?) lightning (< 1 sec) Others - rotation (hours to days), plus other intrinsic variability (clouds, seasons, etc.) Distance may change appreciably (need common distance measurements) These must be dealt with.

10 Time Variability - an example Mars radar snapshots made every 10 mins Butler, Muhleman & Slade 1994

11 Time Variability - an example Mars radar snapshots made every 10 mins Butler, Muhleman & Slade 1994

12 Implications Often can t use same calibrators Often can t easily add together data from different days Solar confusion Other confusion sources move in the beam Antenna and phase center pointing must be tracked (must have accurate ephemeris) Scheduling/planning - need a good match of source apparent size and interferometer spacings

13 Source Strength & Coherence Some solar system bodies are very bright. They can be so bright that they raise the antenna temperature: - Sun ~ 6000 K (or brighter) - Moon ~ 200 K - Venus, Jupiter ~ 1-100s of K In the case of the Sun, special hardware may be required. In other cases, special processing may be needed (e.g., Van Vleck correction). In all cases, the system temperature (the noise) is increased. Some types of emission from the Sun are coherent. In addition, reflection from planetary bodies in radar experiments is coherent (over at least part of the image). This complicates the interpretation of images made of these phenomena, and in fact violates one of the fundamental assumptions in radio interferometry.

14 Source Distance - Wave Curvature Objects which are very close to the Earth may be in the near-field of the interferometer. In this case, there is the additional complexity that the received radiation cannot be assumed to be a plane wave. Because of this, an additional phase term in the relationship between the visibility and sky brightness - due to the curvature of the incoming wave - becomes significant. This phase term must be accounted for at some stage in the analysis.

15 Short Spacing Problem As with other large, bright objects, there is usually a serious short spacing problem when observing the planets. This can produce a large negative bowl in images if care is not taken. This can usually be avoided with careful planning, and the use of appropriate models during imaging and deconvolution.

16 Source Knowledge There is an advantage in most solar system observations - we have a very good idea of what the general source characteristics are, including general expected flux densities and extent of emission. This can be used to great advantage in the imaging, deconvolution, and self-calibration stages of data reduction.

17 Conversion of Coordinates If we know the observed object s geometry well enough, then sky coordinates can be turned into planetographic surface coordinates - which is what we want for comparison, e.g., to optical images.

18 Conversion of Coordinates

19 Correcting for Rotation If a planet rotates rapidly, we can either just live with the smearing in the final image (but note also that this violates our assumption about sources not varying), or try to make snapshots and use them separately (difficult in most cases because SNR is low). There are now two techniques to try to solve this problem; one for optically thin targets like Jupiter synchrotron radiation (Sault et al. 1997; Leblanc et al. 1997; de Pater & Sault 1998), one for optically thick targets (described in Sault et al. 2004). This is possible because we know the viewing geometry and planetary cartographic systems precisely.

20 Correcting for Rotation - Jupiter Jupiter at 20 cm (de Pater et al. 1997) and 1.3 cm (Butler et al. 2009) averaged over full track (period is ~10h):

21 Correcting for Rotation - Jupiter Jupiter at 2, 3.5, and 6 cm from a more recent VLA observation (de Pater et al. 2016) showing the dramatic increase in sensitivity of the VLA:

22 Correcting for Rotation - Jupiter Jupiter at 2cm from several tracks - Sault et al. 2004:

23 Correcting for Rotation - Jupiter Jupiter at 1.3cm from a more recent observation de Pater et al showing the dramatic increase in sensitivity of the VLA:

24 Correcting for Rotation - Jupiter If the emission mechanism is optically thin (this is only the case for the synchrotron emission), then we can make a full 3-D reconstruction of the emission:

25 Correcting for Rotation - Jupiter

26 Spectral Lines Species in the atmospheres of planets form spectral lines, just as they do in other astronomical sources. The strength of the line is proportional to the molecular abundance. The line shape can be written: f (n) = 1 p γ ~ p * 3 MHz/mbar, so for the giant planets, where we are probing down to at least 1 bar pressure, the line widths are many GHz! g ( ) 2 +g 2 n -n 0

27 Spectral Lines Venus Example By knowing the geometry, we can get both abundances and winds as a function of latitude, or time of day, for Venus. Moullet et al. 2012

28 Spectral Lines Mars Example Similarly, we can get water vapor abundances on Mars as a function of latitude and time of day, or season. Butler et al Clancy et al. 1992

29 Lack of Source Knowledge If the true source position is not where the phase center of the instrument was pointed, then a phase error is induced in the visibilities. If you don t think that you knew the positions beforehand, then the phases can be fixed. If you think you knew the positions beforehand, then the phases may be used to derive an offset.

30 Expected Flux Density For optically thick objects with small brightness temperature (most solar system bodies), we must take into account the fact that the body blocks out the background radiation. The expected flux density is: S = (B p - B bg )W p For body brightness B p and solid angle Ω p. B bg is the brightness of the background, which is mostly the CMB and galactic emission. Since the magnitude of the background brightness (at least that of the K CMB) is a significant fraction of the brightness of most solar system objects, this effect must be accounted for when deriving brightness temperature (the interesting physical quantity) from the measured flux density.

31 Real Data - what to expect But They re all round!

32 Real Data - what to expect If the sky brightness is circularly symmetric, then the 2-D Fourier relationship between sky brightness and visibility reduces to a 1-D Hankel transform: V(q) = 2pR For a uniform disk of total flux density F, this reduces to: V(b) = Fp R 2 J 1 (2pb) pb ò 0 R A(r)I(r)J 0 (2prq)r dr and for a limb-darkened disk (of a particular form), this reduces to: V(b) = FpR 2 L q (2pb)

33 Real Data - what to expect Theoretical visibility functions for a circularly symmetric uniform disk and 2 limb-darkened disks.

34 Short Spacing Problem Revisited True visibility function True sky brightness True Measured Missing Measured True Missing Measured True Missing

35 Real Data - polarization For emission from solid surfaces on planetary bodies, the relationship between sky brightness and polarized visibility becomes (again assuming circular symmetry) a different Hankel transform (order 2): V p (b) = ò 1 0 A(r)(R - R^ )J 2 (2prb)rdr this cannot be solved analytically. Note that roughness of the surface is a confusion (it modifies the effective Fresnel reflectivities). For circular measured polarization, this visibility is formed via: V p = Â{V RL + V LR }cos2y + Á{V RL - V LR }sin2y V 0

36 Real Data - polarization Examples of expected polarization response:

37 Real Data - measured Visibility data for an experiment observing Venus at AU distance in the VLA C configuration at 15 GHz:

38 Real Data - an example The resultant image:

39 Real Data - an example Venus models at C, X, Ku, and K-bands:

40 Real Data - an example Venus residual images at U- and K-bands:

41 Real Data - a polarization example Mitchell & de Pater (1994) observations of Mercury showing the polarization pattern on the sky:

42 Real Data - a polarization example Similarly for Mars (Perley & Butler 2013):